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Coordinating Qualitative Predictor Variables in an Applied Linear Model: Analysis and Application for Applied

Wan Muhamad Amir W Ahmad1, Faraz Ahmed2, Mohamad N Adnan3

  • 1Dental Sciences, Universiti Sains Malaysia, Kelantan, MYS.

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Summary
This summary is machine-generated.

This study enhances statistical models by integrating qualitative predictors using dummy variables, fuzzy regression, and Multilayer Feedforward Neural Networks (MLFFNN). The combined approach improves prediction accuracy in applied sciences.

Keywords:
bootstrappingfuzzy regressionhybrid methodologylinear regressionmlffnnqualitative predictors

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Area of Science:

  • Applied Sciences
  • Statistical Modeling
  • Data Analysis

Background:

  • Statistical models are crucial for analyzing complex datasets in applied sciences.
  • Integrating qualitative predictors into linear models presents challenges.
  • Existing methods like dummy variables, MLFFNN, and fuzzy regression offer partial solutions.

Purpose of the Study:

  • To enhance the integration of qualitative predictors into applied linear models.
  • To develop a robust statistical methodology for improved predictive modeling.
  • To validate the proposed approach using advanced statistical techniques.

Main Methods:

  • Transformation of qualitative predictors into dummy variables.
  • Application of the bootstrapping technique for parameter estimation.
  • Utilizing Multilayer Feedforward Neural Networks (MLFFNN) and fuzzy regression.
  • Analysis conducted using the R programming language.

Main Results:

  • Multiple linear regression showed a significant fit (R-squared=0.95, MSE=9.97).
  • Fuzzy regression demonstrated superior predictability compared to standard linear regression.
  • MLFFNN achieved a reduced MSE of 0.362, indicating high prediction precision.

Conclusions:

  • A precise methodology for integrating qualitative variables into linear regression was presented.
  • The combination of fuzzy regression, MLFFNN, and bootstrapping offers the most effective modeling and prediction approach.
  • The proposed technique significantly enhances the accuracy and prediction capabilities of linear models with qualitative predictors.